Calculate the mean deviation about median for the following data:
Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Frequencies: 6, 7, 15, 16, 4, 2

Question

Accepted Answer

>

> [!TLDR]
> Find the median class using cumulative frequency, compute the median, then find the mean of the absolute deviations of each class mark from the median, weighted by frequency.
>
> | Class | $f$ | cf | Midpoint $x$ | $\lvert x-	ext{median}vert$ | $f\lvert x-	ext{median}vert$ |
> |---|---|---|---|---|---|
> | 0-10 | 6 | 6 | 5 | 23 | 138 |
> | 10-20 | 7 | 13 | 15 | 13 | 91 |
> | 20-30 | 15 | 28 | 25 | 3 | 45 |
> | 30-40 | 16 | 44 | 35 | 7 | 112 |
> | 40-50 | 4 | 48 | 45 | 17 | 68 |
> | 50-60 | 2 | 50 | 55 | 27 | 54 |
>
> $N = 6+7+15+16+4+2 = 50$, so $\dfrac N2 = 25$.
>
> **Median class:** The class whose cumulative frequency first reaches or exceeds $25$ is $20	ext{-}30$ (cf $=28$).
> …

Q.Calculate the mean deviation about median for the following data:
Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Frequencies: 6, 7, 15, 16, 4, 2

Concept understanding — Mean Deviation about the Mean and Median

Class	$f$	cf	Midpoint $x$	$\lvert x-\text{median}\rvert$	$f\lvert x-\text{median}\rvert$
0-10	6	6	5	23	138
10-20	7	13	15	13	91
20-30	15	28	25	3	45
30-40	16	44	35	7	112
40-50	4	48	45	17	68
50-60	2	50	55	27	54

Q.Calculate the mean deviation about median for the following data: Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60 Frequencies: 6, 7, 15, 16, 4, 2

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Q.Calculate the mean deviation about median for the following data:
Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Frequencies: 6, 7, 15, 16, 4, 2

Unlock everything free for 14 days