Using the same distribution as Example 3, calculate the mode: | Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | |---|---|---|---|---|---| | No. of students | 5 | 8 | 12 | 10 | 5 |

Using the same distribution as Example 3, calculat – Class 11 Statistics

Worked Examples · Example 6

Using the same distribution as Example 3, calculate the mode:

Marks	0-10	10-20	20-30	30-40	40-50
No. of students	5	8	12	10	5

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The highest frequency is 12, in the class 20-30 — this is the modal class.

$L=20$ , $f_1=12$ (modal class), $f_0=8$ (preceding class, 10-20), $f_2=10$ (succeeding class, 30-40), $h=10$ :

\text{Mode} = L + \left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h = 20 + \left(\frac{12-8}{2(12)-8-10}\right)\times10 = 20+\left(\frac{4}{6}\right)\times10 = 20+6.67 = 26.67

Independent cross-check — empirical relationship: from Examples 3 and 4, Mean $=25.5$ and Median $=25.83$ for this same distribution.

$\text{Mode} \approx 3\,\text{Median} - 2\,\text{Mean} = 3(25.83) - 2(25.5) = 77.5-51 = 26.5$ …

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

CBSE 2024Set ANNUAL1 markMCQ
$Q. From the following, the one which is a positional average, is :$
(a) Arithmetic mean
(b) Geometric mean
(c) Harmonic mean
(d) Mode
›Reveal solutionSolution
Mode is a positional average; the three means are mathematical averages.

Averages are grouped as:

Mathematical averages — computed from the values: arithmetic mean, geometric mean, harmonic mean. …
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CBSE 2024Set ANNUAL1 mark
$Q. Express each of the following in one word / term : A measure of central value which has greatest frequency density.$
›Reveal solutionSolution

One-word term: Mode.

The mode is the value that appears most often; in a frequency distribution it corresponds to the point/class of greatest f …

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CBSE 2023Set ANNUAL1 mark
$Q. Express each of the following in one word / term : A series with two modal values$
›Reveal solutionSolution

A series with two modal values is a bimodal series.

The mode is the value that occurs most frequently. When a series has a single mode it is unimodal; when it has two values that occur with the (equal) highest frequency it is called a **bimodal …

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CBSE 2022Set ANNUAL1 markMCQ
$Q. The value that occurs most often is called :$
(a) Geometric mean
(b) Harmonic mean
(c) Median
(d) Mode
›Reveal solutionSolution
Mode = the value with the highest frequency.

Among the measures of central tendency:

Geometric mean and Harmonic mean are computed averages,

Median is the middle value, …
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CBSE 2022Set ANNUAL1 markMCQ
$Q. The modal value of 6, 7, 8, 9, 8, 7, 8, 9, 8 is :$
(a) $6$
(b) $7$
(c) $8$
(d) $9$
›Reveal solutionSolution
Frequency of $8$ is highest ⇒ mode $=8$ .

Tally the values:

$6$ : once,

$7$ : twice,

$8$ : four times,

$9$ : twice. …
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←Previous questionExample 5 — Find the median of the following discrete series: | x | 10 | 20 | 30 |…→Next questionExample 7 — Find the geometric mean of the observations 2, 4 and 8, both directly …

Concept understanding — Mode

Mode: The Most Frequent Value

The Precise Definition

Examples

Why Mode Matters

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