Question

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Answer 1

Answer:

(a) Mean = 42.6

(b) Median = 37

(c) Mode = Multimodal, All observation has same frequency.

(d) Midrange = 31.5

(e) B.  The mean and median give two different interpretations of the average​ (or typical) jersey​ number, while the midrange shows the spread of possible jersey numbers.

Step-by-step explanation:

The formula used for calculating mean is:

(a) Mean = $\dfrac{\text{Sum of all the observation}}{\text{Total number of observtions}} \\=\dfrac{60+31+19+55+21+37+94+62+41+15+34}{11} \\\Rightarrow Mean = 42.6$

(b) Median is the middle observation after arranging the data in ascending or descending order.

Median is calculate by following steps:

Arranging the data in ascending order: 15, 19, 21, 31, 34, 37, 41, 55, 60, 62, 94.

Median = $(\frac{11+1}{2})^{th} term = 6^{th} term = 37$

(c) Mode is the observation that has highest number of repetitions.

Here every observation has one frequency. So it is multimodal data.

(d) Midrange is also known as Quartile. And it is calculated as difference of Third Quartile to the First Quartile.

Further,  Third Quartile is the middle value of Median and Last value of the observation of ascending order data.

Third Quartile = Q₃ = 57.50

First Quartile is the middle value of the First Value and Median of the observation of ascending order data.

First Quartile = Q₁ = 26

∴ Midrange = 57.50 - 26 = 31.5

(e) Mean, Median and Mode are the three of measure of central tendency from five measure of central tendency and Midrange is used to calculate dispersion\spread\scatter of data. Thus, Option B is only correct option.