Name: Mean of Grouped Data: Example
Uploaded: 2019-07-19
Duration: 5 min 16 s
Description: Want to find out how to calculate the mean of grouped data when the class intervals are different? Watch this interesting video and learn more!

Question

Find the median from the given frequency distribution.

Class Interval	$70 - 74$	$75 - 79$	$80 - 84$	$85 - 89$	$90 - 94$	$95 - 99$	$105 - 109$	$110 - 114$	$115 - 119$
Frequency	$15$	$25$	$30$	$4$	$10$	$8$	$6$	$4$	$3$

Accepted Answer

Given data is

Class Interval

$70 - 74$

$75 - 79$

$80 - 84$
$85 - 89$
$90 - 94$
$95 - 99$
$105 - 109$
$110 - 114$
$115 - 119$

Frequency $15$ $25$ $30$ $4$ $10$ $8$ $6$ $4$ $3$

Now, let prepare the cumulative frequency distribution table for the given data,

Class Interval Frequency Cumulative frequency

$69.5 - 74.5$ $15$ $15$

$74.5 - 79.5$ $25$ $15 + 25 = 40$

$79.5 - 84.5$ $95 - 99$ $40 + 30 = 70$

$84.5 - 89.5$ $4$ $70 + 4 = 74$

$89.5 - 94.5$ $10$ $10 + 74 = 84$

$94.5 - 99.5$ $8$ $84 + 8 = 93$

$99.5 - 105.5$ $6$ $93 + 6 = 99$

$105.5 - 109.5$ $4$ $99 + 4 = 103$

$109.5 - 114.5$ $3$ $103 + 3 = 106$

$N = \sum_{} f = 106$ $\frac{N}{2} = \frac{106}{2} = 53$

$∴$ Median $= l + \frac{\frac{N}{2} - F}{f_{m}} \times i$ , where $l$ is the boundary of the median class, $F$ is the cumulative frequency of the class preceding the median class, $f_{m}$ is the frequency of the median class, $i$ is the length of the median class, $N =$ Total frequency

Here, $l = 79.5, F = 40, f_{m} = 30, i = 79.5 - 84.5 = 5, N = 106$

On substituting the values, we get,

Median $= 79.5 + \frac{53 - 40}{30} \times 5$

$= 79.5 + \frac{13}{6}$

$= 81.6$

Hence, the median for the given data is $81.6$ .

Mid-value	$15$	$25$	$35$	$45$	$55$	$65$	$75$	$85$	$95$
Frequency	$6$	$8$	$10$	$2$	$4$	$7$	$9$	$4$	$6$

Height $(cm)$	$161 - 167$	$167 - 173$	$173 - 179$	$179 - 185$	$185 - 191$	$191 - 197$
Number of students	$79$	$92$	$60$	$22$	$5$	$3$

Weight $(kg)$	$46 - 48$	$49 - 51$	$52 - 54$	$55 - 57$	$58 - 60$
Number of girls	$5$	$8$	$15$	$x$	$4$

Class boundary	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$12$	$30$	$x$	$65$	$y$	$25$	$18$

Class	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Frequency	$5$	$12$	$18$	$28$	$17$	$12$	$8$

Find the median from the given frequency distribution.

Class Interval

$70 - 74$

$75 - 79$

$80 - 84$
$85 - 89$
$90 - 94$
$95 - 99$
$105 - 109$
$110 - 114$
$115 - 119$

Frequency $15$ $25$ $30$ $4$ $10$ $8$ $6$ $4$ $3$

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

Measurement $(x)$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$
Frequency $(f)$	$3$	$4$	$5$	$3$	$5$	$4$	$3$	$2$

Find the median from the given frequency distribution. Class Interval 70-74 75-79 80-84 85-89 90-94 95-99 105-109 110-114 115-119 Frequency 15 25 30 4 10 8 6 4 3

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

Find the median from the given frequency distribution.

Class Interval

$70 - 74$

$75 - 79$

$80 - 84$
$85 - 89$
$90 - 94$
$95 - 99$
$105 - 109$
$110 - 114$
$115 - 119$

Frequency $15$ $25$ $30$ $4$ $10$ $8$ $6$ $4$ $3$