Advertisements
Advertisements
Question
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
| Weight (in kg) | 40−45 | 45−50 | 50−55 | 55−60 | 60−65 | 65−70 | 70−75 |
| Number of students | 2 | 3 | 8 | 6 | 6 | 3 | 2 |
Solution
The cumulative frequencies with their respective class intervals are as follows
| Weight (in kg) | Frequency (fi) | Cumulative frequency |
| 40 − 45 | 2 | 2 |
| 45 − 50 | 3 | 2 + 3 = 5 |
| 50 − 55 | 8 | 5 + 8 = 13 |
| 55 − 60 | 6 | 13 + 6 = 19 |
| 60 − 65 | 6 | 19 + 6 = 25 |
| 65 − 70 | 3 | 25 + 3 = 28 |
| 70 − 75 | 2 | 28 + 2 = 30 |
| Total (n) | 30 |
Cumulative frequency just greater than `N/2 (i.e 30/2 = 15)` is 19, belonging to class interval 55 − 60.
Median class = 55 − 60
Lower limit (l) of median class = 55
Frequency (f) of median class = 6
Cumulative frequency (cf) of median class = 13
Class size (h) = 5
Median = `l + ((N/2 - cf)/f) xx h`
= `55 + ((15-13)/6) xx 5`
= `55 + 10/6`
= 55 + 1.66
= 56.67
Therefore, the weight is 56.67 kg.
APPEARS IN
RELATED QUESTIONS
The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day :
| Age (in years) | No. of Patients |
| 10-20 | 60 |
| 20-30 | 42 |
| 30-40 | 55 |
| 40-50 | 70 |
| 50-60 | 53 |
| 60-70 | 20 |
Find the median age of the patients.
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
| Number of letters | Number of surnames |
| 1 - 4 | 6 |
| 4 − 7 | 30 |
| 7 - 10 | 40 |
| 10 - 13 | 6 |
| 13 - 16 | 4 |
| 16 − 19 | 4 |
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.
The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x
Calculate the median from the following data:
| Marks below: | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
| No. of students: | 15 | 35 | 60 | 84 | 96 | 127 | 198 | 250 |
Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
| Age in years | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| No. of persons | 5 | 25 | ? | 18 | 7 |
The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:
| Class interval | Frequency |
| 0 - 100 | 2 |
| 100 - 200 | 5 |
| 200 - 300 | f1 |
| 300 - 400 | 12 |
| 400 - 500 | 17 |
| 500 - 600 | 20 |
| 600 - 700 | f2 |
| 700 - 800 | 9 |
| 800 - 900 | 7 |
| 900 - 1000 | 4 |
Calculate the median from the following frequency distribution table:
| Class | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 | 40 – 45 |
| Frequency | 5 | 6 | 15 | 10 | 5 | 4 | 2 | 2 |
Find the median wages for the following frequency distribution:
| Wages per day (in Rs) | 61 – 70 | 71 – 80 | 81 – 90 | 91 – 100 | 101 – 110 | 111 – 120 |
| No. of women workers | 5 | 15 | 20 | 30 | 20 | 8 |
Find the median from the following data:
| Class | 1 – 5 | 6 – 10 | 11 – 15 | 16 – 20 | 21 – 25 | 26 – 30 | 31 – 35 | 35 – 40 | 40 – 45 |
| Frequency | 7 | 10 | 16 | 32 | 24 | 16 | 11 | 5 | 2 |
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 |
The following frequency distribution table shows the number of mango trees in a grove and their yield of mangoes, and also the cumulative frequencies. Find the median of the data.
| Class (No. of mangoes) |
Frequency (No. of trees) |
Cumulative frequency (less than) |
| 50-100 | 33 | 33 |
| 100-150 | 30 | 63 |
| 150-200 | 90 | 153 |
| 200-250 | 80 | 233 |
| 250-300 | 17 | 250 |
If the difference of Mode and Median of a data is 24, then the difference of median and mean is ______.
If the mean of the following distribution is 3, find the value of p.
| x | 1 | 2 | 3 | 5 | p + 4 |
| f | 9 | 6 | 9 | 3 | 6 |
The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set ______.
In a hospital, weights of new born babies were recorded, for one month. Data is as shown:
| Weight of new born baby (in kg) | 1.4 - 1.8 | 1.8 - 2.2 | 2.2 - 2.6 | 2.6 - 3.0 |
| No of babies | 3 | 15 | 6 | 1 |
Then the median weight is?
Heights of 50 students of class X of a school are recorded and following data is obtained:
| Height (in cm) | 130 – 135 | 135 – 140 | 140 – 145 | 145 – 150 | 150 – 155 | 155 – 160 |
| Number of students | 4 | 11 | 12 | 7 | 10 | 6 |
Find the median height of the students.
Find the median of the following distribution:
| Marks | 0 – 10 | 10 –20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 |
| Number of students | 5 | 8 | 20 | 15 | 7 | 5 |
The monthly expenditure on milk in 200 families of a Housing Society is given below:
| Monthly Expenditure (in ₹) |
1000 – 1500 | 1500 – 2000 | 2000 – 2500 | 2500 – 3000 | 3000 – 3500 | 3500 – 4000 | 4000 – 4500 | 4500 – 5000 |
| Number of families | 24 | 40 | 33 | x | 30 | 22 | 16 | 7 |
Find the value of x and also, find the median and mean expenditure on milk.
The median of first 10 natural numbers is ______.
The following table shows classification of number of workers and number of hours they work in software company. Prepare less than upper limit type cumulative frequency distribution table:
| Number of hours daily | Number of workers |
| 8 - 10 | 150 |
| 10 - 12 | 500 |
| 12 - 14 | 300 |
| 14 - 16 | 50 |
