Question

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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

(i) Find the mode and median of this data.

(ii) Is there more than one mode?


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Answer 1

Answer:

(i) Mode = 38, 43

   Median = 40

(ii) Yes, there are two modes

Step-by-step explanation:

• Mode is the value which occurs the most frequently in the given set of observations.

• Median is the value of the middle term when the observations are arranged in either ascending or descending order.

The given data is :

38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

⇒ The number of observations = 15

Let's arrange in ascending order :

32, 35, 36, 37 , 38 , 38, 38, 40, 42, 43 , 43, 43, 45, 47, 50

38 and 43 are occurred the most times (i.e., three times) among the given observations.

Hence, mode = 38 and 43

∴ There are two modes.

In the given set of observations when arranged in ascending order, the middle most term is 40.

Hence, median = 40

Median can also be calculated by : (if the number of observations is odd)

Median = (number of observations + 1)/2 th term

⇒ Median = (15 + 1)/2 th term

⇒ Median = 16/2 th term

⇒ Median = 8th term

8th term in the given set (after arranging in ascending order) is 40

Hence, median = 40

Answer 2

Arranging the given weights 15 students of a class in an ascending order, we get

32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50

(i) Mode and Median

Mode,

Mode is the value of the variable which occurs most frequently.

Clearly, 38 and 43 both occurs 3 times.

Hence, mode of the given weights are 38 and 43.

Median,

The value of the middle-most observation is called the median of the data.

Here n = 15, which is odd.

Where, n is the number of the students.

∴median = value of ½ (n + 1)th observation.

= ½ (15 + 1)

= ½ (16)

= 16/2

= 8

Then, value of 8th term = 40

Hence, the median is 40.

(ii) Yes, there are 2 modes for the given weights of the students.