Calculate the mean deviation about median for the following data. Class: $0 ext{-}10$, $10 ext{-}20$, $20 ext{-}30$, $30 ext{-}40$, $40 ext{-}50$, $50 ext{-}60$; Frequency: $6$, $7$, $15$, $16$, $4$, $2$

Question

Calculate the mean deviation about median for the following data. Class: $0	ext{-}10$, $10	ext{-}20$, $20	ext{-}30$, $30	ext{-}40$, $40	ext{-}50$, $50	ext{-}60$; Frequency: $6$, $7$, $15$, $16$, $4$, $2$

Accepted Answer

>

> [!TLDR]
> The mean deviation about the median is $10.16$.
>
> | Class | Frequency $f$ | Midpoint $x_i$ | Cumulative frequency |
> |---|---|---|---|
> | $0$-$10$ | $6$ | $5$ | $6$ |
> | $10$-$20$ | $7$ | $15$ | $13$ |
> | $20$-$30$ | $15$ | $25$ | $28$ |
> | $30$-$40$ | $16$ | $35$ | $44$ |
> | $40$-$50$ | $4$ | $45$ | $48$ |
> | $50$-$60$ | $2$ | $55$ | $50$ |
>
> $N = 50$, so $N/2 = 25$. The cumulative frequency first reaching $25$ is $28$, in the class $20$-$30$ — this is the median class ($L=20$, cumulative freq before it $cf=13$, class frequency $f=15$, class width $h=10$).
>
> **Median** $= L + \dfrac{\frac{N}{2}-cf}{f}	imes h = 20+\dfrac{25-13}{15}	imes10 = 20+\dfrac{12}{15}	imes10 = 20+8 = 28$
>
> **Absolute deviations $|x_i - 28|$ and $f|x_i-28|$:**
>
> | $x_i$ | $|x_i-28|$ | $f$ | $f|x_i-28|$ |
> |---|---|---|---|
> | $5$ | $23$ | $6$ | $138$ | …

Q.Calculate the mean deviation about median for the following data. Class: $0\text{-}10$ , $10\text{-}20$ , $20\text{-}30$ , $30\text{-}40$ , $40\text{-}50$ , $50\text{-}60$ ; Frequency: $6$ , $7$ , $15$ , $16$ , $4$ , $2$

Concept understanding — Mean Deviation about the Mean and Median

Class	Frequency $f$	Midpoint $x_i$	Cumulative frequency
$0$ - $10$	$6$	$5$	$6$
$10$ - $20$	$7$	$15$	$13$
$20$ - $30$	$15$	$25$	$28$
$30$ - $40$	$16$	$35$	$44$
$40$ - $50$	$4$	$45$	$48$
$50$ - $60$	$2$	$55$	$50$

Q.Calculate the mean deviation about median for the following data. Class: 0-100\text{-}100-10, 10-2010\text{-}2010-20, 20-3020\text{-}3020-30, 30-4030\text{-}4030-40, 40-5040\text{-}5040-50, 50-6050\text{-}6050-60; Frequency: 666, 777, 151515, 161616, 444, 222

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Q.Calculate the mean deviation about median for the following data. Class: $0\text{-}10$ , $10\text{-}20$ , $20\text{-}30$ , $30\text{-}40$ , $40\text{-}50$ , $50\text{-}60$ ; Frequency: $6$ , $7$ , $15$ , $16$ , $4$ , $2$

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