Data Handling
Exercise 3.2
Question 1: The scores in mathematics test (out of 25) of 15 students is as follows: (19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20) Find the mode and median of this data. Are they same?
Answer: The scores can be arranged as follows:
| Score | Tally marks | No. of Students |
|---|---|---|
| 5 | | | 1 |
| 9 | | | 1 |
| 10 | | | 1 |
| 12 | | | 1 |
| 15 | | | 1 |
| 16 | | | 1 |
| 19 | | | 1 |
| 20 | |||| | 4 |
| 23 | | | 1 |
| 24 | | | 1 |
| 25 | || | 2 |
| Total | 15 |
Score occurring most number of times = 20
Hence, mode = 25
Median can be calculated as follows:
We have odd number of scores = 15
So, position of median
`=(text(Number of scores)+1)/(2)`
`=(15+1)/(2)=8`
The eighth score is shown below in bold:
5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25
Hence, median = 20
In this case, median and mode are same.
Question 2: The runs scored in a cricket match by 11 players is as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Find the mean, mode and median of this data. Are the three same?
Answer: The scores can be arranged in ascending order as follows: (6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120)
| Score | Tally makrs | No. of players |
|---|---|---|
| 6 | | | 1 |
| 8 | | | 1 |
| 10 | || | 2 |
| 15 | ||| | 3 |
| 50 | | | 1 |
| 80 | | | 1 |
| 100 | | | 1 |
| 120 | | | 1 |
| Total | 11 |
Mode = Score appearing most number of times = 15
Median can be calculated as follows:
We have odd number of scores = 11
So, position of median
`=(text(Number of scores)+1)/(2)`
`=(11+1)/(2)=6`
Sixth score = 15
Hence, median = 15
Arithmetic mean can be calculated as follows:
`text(Mean)=text(Sum of each observation)/text(Number of observations)`
=(6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120) ÷ 11
`=(429)/(11)=39`
Question 3: The weights (in kg.) of 15 students of a class are: 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
Answer: The weights can be arranged in ascending order as follows: (32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50)
| Weight (in kg) | Tally marks | No. of students |
|---|---|---|
| 32 | | | 1 |
| 35 | | | 1 |
| 36 | | | 1 |
| 37 | | | 1 |
| 38 | ||| | 3 |
| 40 | | | 1 |
| 42 | | | 1 |
| 43 | ||| | 3 |
| 45 | | | 1 |
| 47 | | | 1 |
| 50 | | | 1 |
| Total | 15 |
(a) Find the mode and median of this data.
Answer: Mode = 38 and 43
Median = 40 (Eighth observation)
(b) Is there more than one mode?
Answer: There are two modes in this data.
Question 4: Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
Answer:
| Observations | Tally marks | No. of observations |
|---|---|---|
| 12 | || | 2 |
| 13 | || | 2 |
| 14 | ||| | 3 |
| 16 | | | 1 |
| 19 | | | 1 |
| Total | 9 |
Mode = 14
Median = 14 (fifth observation)
Question 5: Tell whether the statement is true or false:
(a) The mode is always one of the numbers in a data.
Answer: True; because mode shows the observation appearing for most number of times.
(b) The mean is one of the numbers in a data.
Answer: False; because mean is calculated after adding all the data and dividing the sum with total number of observations.
(c) The median is always one of the numbers in a data.
Answer: True; because median is the data in the middle.
(d) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.
Answer: False: following is the explanation:
`text(Mean)= text(Sum of observations)/text(Number of observations)`
`=(6+4+3+8+9+12+13+9)/(8)`
`=(64)/(8)=8`