(A) Write a user defined function in Python named showGrades(S) which takes the dictionary S as an argument. T

Question 53 of 97

Q. (A) Write a user defined function in Python named showGrades(S) which takes the dictionary S as an argument. The dictionary, S contains Name:[Eng,Math,Science] as key:value pairs. The function displays the corresponding grade obtained by the students according to the following grading rules: Average of Eng, Math, Science Grade >= 90 A < 90 but >= 60 B < 60 C For example: Consider the following dictionary S={"AMIT":[92,86,64],"NAGMA":[65,42,43],"DAVID":[92,90,88]} The output should be: AMIT - B NAGMA - C DAVID - A

(OR)

(B) Write a user defined function in Python named Puzzle(W,N) which takes the argument W as an English word and N as an integer and returns the string where every Nth alphabet of the word W is replaced with an underscore ("_"). For example: if W contains the word "TELEVISION" and N is 3, then the function should return the string "TE_EV_SI_N". Likewise for the word "TELEVISION" if N is 4, then the function should return "TEL_VIS_ON".

Sikkim CbseCBSE Class XII Board 2024Subjective· 2mImportance★★★★★

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Part (a)Concept understanding — Arithmetic Mean

The Arithmetic Mean: Finding the Centre of a Story

Imagine you and your friends are comparing pocket money. One friend gets ₹500, another gets ₹200, a third gets ₹800, and you get ₹300. If someone asked, "What is the typical pocket money in this group?" you wouldn't list all four amounts — you'd want a single number that represents the group fairly. That instinct — to find a middle ground, a representative value — is exactly what the arithmetic mean captures.

The arithmetic mean is the most common way of answering the question: "If everything were shared equally, what would each person get?" It is the balance point of a set of numbers. In everyday language, people call it the "average," though statisticians use "average" as a broader family that includes the mean, median, and mode.

The Precise Meaning

The arithmetic mean is calculated by taking the sum of all the values in a group and then dividing that total by the number of values. It answers the question: "What single value, if repeated for every item, would give the same total as the actual data?"

Think of it as a redistribution. If you had a pile of money equal to the total of all your friends' pocket money, and you wanted everyone to walk away with the same amount, the arithmetic mean is exactly that equal share. It is the number that makes the "total" stay the same while smoothing out the differences.

Note

The arithmetic mean is sensitive to every single value in the data set. If one friend gets an enormous amount of pocket money, the mean gets pulled upward — even if everyone else gets very little. This is why the mean is not always the best representative when there are extreme values (outliers).

Why It Matters

The arithmetic mean is the foundation of almost all statistical thinking. Here is why it is so important:

It gives a single reference point. Instead of describing a whole list of numbers, you can say "the average income in this neighbourhood is ₹40,000 per month." That one number summarises a complex reality.
It allows comparison. You can compare the average test score of one class with another, or the average rainfall in one city with another. Without the mean, you would be comparing entire lists — which is impractical.
It is the basis for further analysis. Many advanced statistical tools — like standard deviation, correlation, and regression — all start from the arithmetic mean. It is the anchor point from which we measure variation and relationships.
It is used in everyday decision-making. Businesses calculate average sales per day to plan inventory. Governments use average income to set policies. Even your own grade point average is an arithmetic mean of your subject marks.

A Few Key Points to Remember …

Part (b)Concept understanding — String Functions

String Functions: A First Look

Think of a string as a piece of text — a word, a sentence, a name, or even a single character. In computing, strings are everywhere: your name in a form, a product code in a database, a tweet, a paragraph in a document. String functions are the tools that let you work with that text: cut it, join it, clean it, search inside it, or change its appearance.

You already use these ideas in everyday life. When you take a long sentence and pick out just the first word, you are performing a "substring" operation. When you combine your first name and last name into a full name, you are "concatenating" two strings. When you check whether an email address contains an "@" symbol, you are "searching" within a string. String functions are just these familiar actions, given precise names and made available in software.

The Core Idea

A string function takes one or more strings as input and returns a new string or a piece of information about the string. The function does not change the original string — it produces a result based on it. This is important: the original data stays untouched unless you explicitly replace it.

Note

Strings are treated as sequences of characters. Each character — letter, digit, space, punctuation — occupies a position. In most systems, counting starts at 1 (the first character is position 1), though some languages start at 0. Always check which convention your tool uses.

Common Types of String Functions

1. Changing Case

These functions convert text to uppercase or lowercase. They are useful when you want to compare names or addresses without worrying about whether someone typed "Delhi" or "delhi".

UPPER or UCASE: converts all letters to capitals
LOWER or LCASE: converts all letters to small letters
PROPER or TITLE: capitalises the first letter of each word

2. Extracting Parts of a String

You often need to pull out a specific portion of text — the first name from a full name, the area code from a phone number, the year from a date.

LEFT: returns a given number of characters from the start
RIGHT: returns a given number of characters from the end
MID or SUBSTRING: returns characters starting from a specified position for a specified length

3. Finding and Replacing

These functions let you search inside text and optionally replace what you find.

FIND or INSTR: locates the position of one string inside another
REPLACE: substitutes all occurrences of a substring with another string
TRIM: removes extra spaces from the beginning and end of a string

4. Joining and Splitting

CONCAT or the ampersand (&): joins two or more strings end to end
SPLIT (in some systems): breaks a string into parts based on a delimiter (like a comma or space)

5. Measuring Length

LEN or LENGTH: returns the number of characters in a string

Why They Matter

In any real-world data task — whether you are cleaning a customer list, generating reports, validating user input, or preparing data for analysis — you will work with text. String functions give you the power to:

Standardise messy data (e.g., "john", "John", "JOHN" all become "John")
Extract meaningful pieces from longer text (e.g., get the domain from an email) …

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Part (a)

Iterate the dictionary, take the average of the three marks and map it to a grade.

def showGrades(S):
    for name, marks in S.items():
        avg = sum(marks) / 3
        if avg >= 90:
            grade = 'A'
        elif avg >= 60:
            grade = 'B'
        else:
            grade = 'C'
        print(name, "-", grade)
``` …

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Part (a) computes each student's average of three marks and prints a grade (A/B/C); Part (b) returns the word with every Nth character replaced by an underscore.

Part (a)

Each key of S is a student name and its value is a list [Eng, Math, Science].

Approach

Loop over S.items() to get each name and its marks list.
avg = sum(marks) / 3.
Grade: avg >= 90 → A, else avg >= 60 → B, else C.
Print name - grade.

def showGrades(S):
    for name, marks in S.items():
        avg = sum(marks) / 3
        if avg >= 90:
            grade = 'A'
        elif avg >= 60:
            grade = 'B'
        else:
            grade = 'C'
        print(name, "-", grade)

S = {"AMIT":[92,86,64], "NAGMA":[65,42,43], "DAVID":[92,90,88]}
showGrades(S)

Trace — AMIT: (92+86+64)/3 = 80.67 → B; NAGMA: 150/3 = 50 → C; DAVID: 270/3 = 90 → A.

AMIT - B
NAGMA - C
DAVID - A …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CA Foundation 2026Set jan-20261 markMCQ
$x+1$
›Reveal solutionSolution

Mean $=x+\dfrac{1+3+5+7+9}{5}=x+5=125\Rightarrow x=120$ .

Step 1 — Sum the observations
$\sum=(x+1)+(x+3)+(x+5)+(x+7)+(x+9)=5x+25.$
Step 2 — Set the mean equal to 125
$\text{Mean}=\frac{5x+25}{5}=x+5=125.$
Step 3 — Solve

$x=125-5=120.$ …
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CA Foundation 2026Set may-20261 markMCQ
$k$
›Reveal solutionSolution

The $k^2$ terms cancel; solving $\dfrac{40+15k}{5}=20$ gives $k=4$ .

Step 1 — Write the mean equation

For the five observations $40,\ k,\ 6k,\ 4k^2,\ 8k-4k^2$ :
$\text{Mean} = \frac{40 + k + 6k + 4k^2 + (8k - 4k^2)}{5} = 20$
Step 2 — Simplify the numerator

The $k^2$ terms cancel and the $k$ terms combine:
$4k^2 - 4k^2 = 0,\qquad k + 6k + 8k = 15k$ $\Rightarrow \text{sum} = 40 + 15k$
Step 3 — Solve for k
$\frac{40 + 15k}{5} = 20 \;\Rightarrow\; 40 + 15k = 100 \;\Rightarrow\; 15k = 60 \;\Rightarrow\; k = 4$
Why the other options are wrong: $k=15,10,8$ give sums of $265,190,160$ and means of $53,38,32$ — none equal $20$ . Only $k=4$ satisfies the equation. …
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CA Foundation 2026Set may-20261 markMCQ
$Q. The mean of five observations is 28. Among the five observations, three observations are 10, 23 and 62. The difference between the remaining two observations is 13. Then the remaining two observations are ______. (A) 30 and 17 (B) 38 and 15 (C) 29 and 16 (D) 35 and 22$
›Reveal solutionSolution

The last two observations sum to $45$ and differ by $13$ , giving $29$ and $16$ .

Step 1 — Find the total sum

Mean $= 28$ over $5$ observations, so
$\sum x = 28 \times 5 = 140$
Step 2 — Subtract the known observations

The three given values total $10 + 23 + 62 = 95$ , so the remaining two satisfy
$x + y = 140 - 95 = 45$
Step 3 — Use the difference and solve

Given $x - y = 13$ , add the two equations:
$2x = 45 + 13 = 58 \;\Rightarrow\; x = 29,\qquad y = 45 - 29 = 16$
Check: $29 + 16 = 45$ ✓ and $29 - 16 = 13$ ✓.

Why the other options are wrong: (A) $30+17=47$ , (B) $38+15=53$ , (D) $35+22=57$ — none sum to the required $45$ , so only $29$ and $16$ fit both conditions. …
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CA Foundation 2026Set may-20261 markMCQ
$Q. Which of the followings is a property of Arithmetic Mean? (A) Sum of deviations from Arithmetic Mean is always positive. (B) Arithmetic Mean is not affected by extreme values. (C) Sum of deviations from Arithmetic Mean is always zero. (D) Arithmetic Mean cannot be calculated for grouped data.$
›Reveal solutionSolution
The algebraic sum of deviations about the arithmetic mean is always zero.

Step 1 — State the property

For observations $x_1,\ldots,x_n$ with mean $\bar{x}$ :
$\sum_{i=1}^{n}(x_i - \bar{x}) = 0$
Step 2 — Show why

Expand the sum:
$\sum (x_i - \bar{x}) = \sum x_i - n\bar{x} = \sum x_i - n\cdot\frac{\sum x_i}{n} = \sum x_i - \sum x_i = 0$
Positive deviations (values above the mean) exactly offset negative deviations (values below it).

Step 3 — Reject the false statements

Sum of deviations is zero, not always positive → (A) is false.

The mean is affected by extreme values → (B) is false.

The mean can be computed for grouped data using $\dfrac{\sum f x}{\sum f}$ → (D) is false.

So only (C) is a genuine property. …
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CA Foundation 2026Set may-20261 markMCQ
$Q. The mean of 10 observations is 15. If one observation 12 is replaced by 22, what will be the new mean? (A) 16 (B) 14 (C) 17 (D) 18$
›Reveal solutionSolution
Change the total by the swap, keep the count the same: new mean $=\dfrac{150-12+22}{10}=16$ .

Step 1 — Recover the original total

Mean $=\dfrac{\text{sum}}{n}$ , so sum $=$ mean $\times n = 15\times 10 = 150$ .

Step 2 — Adjust the total for the replacement

Remove 12 and add 22:
$\text{New sum} = 150 - 12 + 22 = 160$
Step 3 — Recompute the mean
$\text{New mean} = \frac{160}{10} = 16$
Why the other options are wrong

(B) 14 wrongly subtracts the change instead of adding it. …
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CA Foundation 2026Set may-20261 markMCQ
$Q. The given frequency distribution is : X 1234567 Y 59121714106 The arithmetic mean of the Frequency distribution is ________. (A) 2.99 (B) 3.06 (C) 4.10 (D) 4.71$
›Reveal solutionSolution

Weighted mean $=\sum fX/\sum f = 299/73 \approx 4.10$ .

Step 1 — Set up the formula

X are the values and Y are their frequencies (f), so the arithmetic mean of the frequency distribution is:
$\bar{X}=\dfrac{\sum fX}{\sum f}$
Step 2 — Compute $\sum f$ and $\sum fX$

X f fX
1 5 5
2 9 18
3 12 36
4 17 68
5 14 70
6 10 60
7 6 42
Total 73 299

Step 3 — Divide

$\bar{X}=\dfrac{299}{73}=4.0959\approx 4.10$ …
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CA Foundation 2025Set jan-20251 markMCQ
$Q. The mean of three numbers is 135. Among the three numbers the biggest number is 180. The difference between the remaining two numbers is 25. Then the smallest number is (A) 130 (B) 125 (C) 120 (D) 100$
›Reveal solutionSolution

Sum of all three $=405$ ; the other two total $225$ and differ by $25$ , giving $125$ and $100$ — smallest is $100$ .

Step 1 — Find the total from the mean
$\text{Sum} = \text{Mean}\times n = 135\times 3 = 405$
Step 2 — Isolate the remaining two numbers

The biggest number is $180$ , so the other two add to
$405 - 180 = 225.$
Step 3 — Split using the difference

Let the two numbers be $a$ and $b$ with $a+b=225$ and $a-b=25$ .
$a = \dfrac{225+25}{2}=125,\qquad b=\dfrac{225-25}{2}=100.$
Both are below the biggest value $180$ , so the data is consistent and the smallest number is $100$ . …
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CA Foundation 2025Set jan-20251 markMCQ
$\dfrac{\Sigma x_i}{n}$
›Reveal solutionSolution

$\sum(x_i-\bar{x})=0$ : deviations about the arithmetic mean always sum to zero.

Step 1 — Write the sum of deviations
$\sum_{i=1}^{n}(x_i-\bar{x}) = \sum x_i - n\bar{x}.$
Step 2 — Substitute the mean

Since $\bar{x}=\dfrac{\sum x_i}{n}$ , we have $n\bar{x}=\sum x_i$ , so
$\sum(x_i-\bar{x}) = \sum x_i - \sum x_i = 0.$
This is a defining property of the arithmetic mean — it is the point of balance of the data.

Why the other options are wrong: $\dfrac{\sum x_i}{n}$ (A) is the mean itself, (B) is the sample standard deviation, and (C) is a mis-formed average — none equals the sum of deviations. …
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CA Foundation 2025Set may-20251 markMCQ
$Q. If the mean of the following frequency distribution is 2.6, then the value of Y is Marks (X) 12345 No. of Students$
(f) | 8 | 10 | Y | 2 | 4 | (A) 16 (B) 6 (C) 26 (D) 12
›Reveal solutionSolution

Set the mean formula equal to 2.6 and solve for Y: $Y = 16$ .

Step 1 — Build Σf and Σfx

Marks (X) 1 2 3 4 5
f 8 10 Y 2 4
fX 8 20 3Y 8 20
$\Sigma f = 24 + Y,\qquad \Sigma fX = 56 + 3Y.$
Step 2 — Apply the mean formula
$\bar X = \dfrac{\Sigma fX}{\Sigma f} = 2.6 \;\Rightarrow\; \dfrac{56+3Y}{24+Y} = 2.6.$
Step 3 — Solve
$56 + 3Y = 2.6(24+Y) = 62.4 + 2.6Y$
$3Y - 2.6Y = 62.4 - 56 \;\Rightarrow\; 0.4Y = 6.4 \;\Rightarrow\; Y = 16.$ …
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CA Foundation 2025Set sep-20251 markMCQ
$Q. A set contains seven numbers whose average is 12. The average of four greater numbers is 18 and the average of four smaller numbers is 8. Which of the followings is the value of one of the numbers ? (A) 12 (B) 16 (C) 18 (D) 20$
›Reveal solutionSolution

The middle number is shared by both the 'four greater' and 'four smaller' sets: 72 + 32 − 84 = 20.

Step 1 — Total of all seven
$\text{Sum of 7} = 7 \times 12 = 84$
Step 2 — Totals of the two overlapping groups
$\text{Four greater} = 4 \times 18 = 72, \qquad \text{Four smaller} = 4 \times 8 = 32$
These two groups name $4 + 4 = 8$ positions, but there are only 7 numbers, so exactly one number belongs to both groups (the 4th, or middle, number).

Step 3 — Find the shared number

By inclusion–exclusion, sum of the two groups counts the shared number twice:
$72 + 32 = 84 + (\text{shared number})$
$\text{shared number} = 104 - 84 = 20$ …
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X	1	2	3	4	5	6	7
Y	5	9	12	17	14	10	6

X	f	fX
1	5	5
2	9	18
3	12	36
4	17	68
5	14	70
6	10	60
7	6	42
Total	73	299

Marks (X)	1	2	3	4	5
f	8	10	Y	2	4
fX	8	20	3Y	8	20

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Part (a)

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