Advertisements
Advertisements
Question
The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows:
| Speed (km/h) | 85 – 100 | 100 – 115 | 115 – 130 | 130 – 145 |
| Number of players | 11 | 9 | 8 | 5 |
Calculate the median bowling speed.
Solution
First we construct the cumulative frequency table
| Speed (in km/h) |
Number of players |
Cumulative frequency |
| 85 – 100 | 11 | 11 |
| 100 – 115 | 9 | 11 + 9 = 20 |
| 115 – 130 | 8 | 20 + 8 = 28 |
| 130 – 145 | 5 | 28 + 5 = 33 |
It is given that, n = 33
∴ `n/2 = 33/2 = 16.5`
So, the median class is 100 – 115.
Where, lower limit (l) = 100,
Frequency (f) = 9,
Cumulative frequency (cf) = 11
And class width (h) = 15
∴ Median = `l + ((n /2 - cf))/f xx h`
= `100 + ((16.5 - 11))/9 xx 15`
= `100 + (5.5 xx 15)/9`
= `100 + 82.5/9`
= 100 + 9.17
= 109.17
Hence, the median bowling speed is 109.17 km/h.
APPEARS IN
RELATED QUESTIONS
The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:
| Length (in mm) | Number of leaves |
| 118 − 126 | 3 |
| 127 – 135 | 5 |
| 136 − 144 | 9 |
| 145 – 153 | 12 |
| 154 – 162 | 5 |
| 163 – 171 | 4 |
| 172 – 180 | 2 |
Find the median length of the leaves.
(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 − 126.5, 126.5 − 135.5… 171.5 − 180.5)
If the median of the distribution given below is 28.5, find the values of x and y.
| Class interval | Frequency |
| 0 - 10 | 5 |
| 10 - 20 | x |
| 20 - 30 | 20 |
| 30 - 40 | 15 |
| 40 - 50 | y |
| 50 - 60 | 5 |
| Total | 60 |
Compute the median for the following data:
| Marks | No. of students |
| More than 150 | 0 |
| More than 140 | 12 |
| More than 130 | 27 |
| More than 120 | 60 |
| More than 110 | 105 |
| More than 100 | 124 |
| More than 90 | 141 |
| More than 80 | 150 |
The marks obtained by 19 students of a class are given below:
27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and 28.
Find:
- Median
- Lower quartile
- Upper quartile
- Inter-quartile range
From the following data, find:
Upper quartile
25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83
The following frequency distribution table gives the ages of 200 patients treated in a hospital in a week. Find the mode of ages of the patients.
| Age (years) | Less than 5 | 5 - 9 | 10 - 14 | 15 - 19 | 20 - 24 | 25 - 29 |
| No. of patients | 38 | 32 | 50 | 36 | 24 | 20 |
Which measure of central tendency can be determine graphically?
Will the median class and modal class of grouped data always be different? Justify your answer.
The median of the following frequency distribution is 25. Find the value of x.
| Class: | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
| Frequency: | 6 | 9 | 10 | 8 | x |
A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:
| Family size | 1 – 3 | 3 – 5 | 5 – 7 | 7 – 9 | 9 – 11 |
| Numbers of Families | 7 | 8 | 2 | 2 | 1 |
Find the median of this data.
