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:

ScoreTally marksNo. of Students
5|1
9|1
10|1
12|1
15|1
16|1
19|1
20||||4
23|1
24|1
25||2
Total15

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)

ScoreTally makrsNo. of players
6|1
8|1
10||2
15|||3
50|1
80|1
100|1
120|1
Total11

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 marksNo. of students
32|1
35|1
36|1
37|1
38|||3
40|1
42|1
43|||3
45|1
47|1
50|1
Total15

(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:

ObservationsTally marksNo. of observations
12||2
13||2
14|||3
16|1
19|1
Total9

Mode = 14
Median = 14 (fifth observation)

Question 5: Tell whether the statement is true or false:

  1. The mode is always one of the numbers in a data.

    Answer: True; because mode shows the observation appearing for most number of times.
  2. 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.
  3. The median is always one of the numbers in a data.

    Answer: True; because median is the data in the middle.
  4. 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`


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