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

The annual rainfall record of a city for $66$ days is given in the following table.

Rainfall (in cm)	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Number of days	$22$	$10$	$8$	$15$	$5$	$6$

Calculate the median rainfall using ogives (or more than type and less than type).

Accepted Answer

We observe that, the annual rainfall record of a city less than $0$ is $0$ . Similarly, less than $10$ include the annual rainfall record of a city from $0$ as well as the annual rainfall record of a city from $0 - 10$ .

So, the total annual rainfall record of a city for less than $10 cm$ is $0 + 22 = 22$ days.

Continuing in this manner, we will get remaining less than $20, 30, 40, 50$ and $60$ .

Also, we observe that annual rainfall record of a city for $22$ days is more than or equal to $0 cm$ . Since, $22$ days lie in the interval $0 - 10$ . So, annual rainfall record for $66 - 22 = 44$ days is more than or equal to $10 cm$ . Continuing in this manner we will get remaining more than or equal to $20, 30, 40, 50$ and $60$ .

Now, we construct a table for less than and more than types.

(i) Less than type (ii) More than type

Rainfall (in cm Number of days Rainfall (in cm Number of days

Less than $0$ $0$ More than or equal to $0$ $66$

Less than $10$ $0 + 22 = 22$ More than or equal to $10$ $66 - 22 = 44$

Less than $20$ $22 + 10 = 32$ More than or equal to $20$ $44 - 10 = 34$

Less than $8$ $15$ More than or equal to $30$ $34 - 8 = 26$

Less than $40$ $40 + 15 = 55$ More than or equal to $40$ $26 - 15 = 11$

Less than $50$ $55 + 5 = 60$ More than or equal to $50$ $11 - 5 = 6$

Less than $60$ $60 + 6 = 66$ More than or equal to $60$ $6 - 6 = 0$

To draw less than type ogive we plot the points $(0, 0), (10, 22), (20, 32), (30, 40), (40, 55), (50, 60), (60, 66)$ on the paper and join them by free hand.

To draw more than type ogive we plot the points $(0, 66), (10, 44), (20, 34), (30, 26), (40, 11), (50, 6), (60, 0)$ on the graph paper and join them by free hand.

Total number of days $(n) = 66$

Now, $\frac{n}{2} = 33$

Firstly, we plot a line parallel to $x$ - axis at intersection point of both ogives, which further intersect at $(0, 33)$ on $y$ - axis. Now, we draw a line perpendicular to $x$ - axis at intersection point of both ogives, which further intersect at $(21.25, 0)$ on $x$ - axis. Which is the required median using ogives.

Hence, median rainfall $= 21.25 cm$

Duration (in s)	Number of calls
$95 - 125$	$14$
$125 - 155$	$22$
$155 - 185$	$28$
$6 - 6 = 0$	$21$
$215 - 245$	$15$

Distance (in m)	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Number of students	$6$	$11$	$17$	$12$	$4$

Distance (in m)	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Number of students	$6$	$11$	$17$	$12$	$4$

Distance (in m)	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Number of students	$6$	$11$	$17$	$12$	$4$

Distance (in m)	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Number of students	$6$	$11$	$17$	$12$	$4$

The annual rainfall record of a city for $66$ days is given in the following table.

Rainfall (in cm) $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$

Number of days $22$ $10$ $8$ $15$ $5$ $6$

Calculate the median rainfall using ogives (or more than type and less than type).

Important Questions on Statistics and Probability

Learn and Prepare for any exam you want !

The annual rainfall record of a city for 66 days is given in the following table. Rainfall (in cm) 0-10 10-20 20-30 30-40 40-50 50-60 Number of days 22 10 8 15 5 6 Calculate the median rainfall using ogives (or more than type and less than type).

Important Questions on Statistics and Probability

Learn and Prepare for any exam you want !

The annual rainfall record of a city for $66$ days is given in the following table.

Rainfall (in cm) $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$

Number of days $22$ $10$ $8$ $15$ $5$ $6$

Calculate the median rainfall using ogives (or more than type and less than type).