Advertisements
Advertisements
Question
The median of the following observations 11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean.
Solution
11, 12, 14, (x – 2), (x + 4), (x + 9), 32, 38, 47
n = 9, odd
∴ Median = `((9 + 1)/(2))^(th)`
24 = 5th observation = (x + 4)
24 = x + 4 ...(As median = 24)
24 – 4 = x
`=>` x = 20
∴ Observation are 11, 12, 14, (20 – 2), (20 + 4), (20 + 9), 32, 38, 47
or
11, 12, 14, 18, 24, 29, 32, 38, 47
Mean = `barX`
= `(11 + 12 + 14 + 18 + 24 + 29 + 32 + 38 + 47)/(9)`
= `(225)/(9)`
= 25
APPEARS IN
RELATED QUESTIONS
The following is the distribution of height of students of a certain class in a certain city:
| Height (in cm): | 160 - 162 | 163 - 165 | 166 - 168 | 169 - 171 | 172 - 174 |
| No. of students: | 15 | 118 | 142 | 127 | 18 |
Find the median height.
Calculate the median from the following data:
| Rent (in Rs.): | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 | 75 - 85 | 85 - 95 |
| No. of Houses: | 8 | 10 | 15 | 25 | 40 | 20 | 15 | 7 |
An incomplete distribution is given below:
| Variable: | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency: | 12 | 30 | - | 65 | - | 25 | 18 |
You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.
The following table shows the daily wages of workers in a factory:
| Daily wages in (Rs) | 0 – 100 | 100 – 200 | 200 – 300 | 300 – 400 | 400 – 500 |
| Number of workers | 40 | 32 | 48 | 22 | 8 |
Find the median daily wage income of the workers.
Find the median from the following data:
| Marks | No of students |
| Below 10 | 12 |
| Below 20 | 32 |
| Below 30 | 57 |
| Below 40 | 80 |
| Below 50 | 92 |
| Below 60 | 116 |
| Below 70 | 164 |
| Below 80 | 200 |
A data has 25 observations arranged in a descending order. Which observation represents the median?
The median of first 10 prime numbers is
The arithmetic mean and mode of a data are 24 and 12 respectively, then its median is
Find a certain frequency distribution, the value of mean and mode are 54.6 and 54 respectively. Find the value of median.
If 35 is removed from the data, 30, 34, 35, 36, 37, 38, 39, 40 then the median increases by ______.
