Question

Mr. Martin gave a test and wants to consider some numbers that will help him decide how well his students did. He wants to know all the M numbers: Maximum, Minimum, Mode, Median and Mean. Look at the test scores below and consider all of the M numbers: Maximum: Minimum: Mode: Median: Mean: Test scores: 75, 85, 56, 72, 98, 75, 64, 88, 62, 87, 85, 75, 99, 42, 88

Answer 1

Answer:

Maximum = 99

Minimum = 42

Mode = 75

Median = 75

Mean = 76.73

Step-by-step explanation:

We are given the test scores below and we have to find all of the M numbers.

Firstly arranging the given test scores in ascending order we get;

42, 56, 62, 64, 72, 75, 75, 75, 85, 85, 87, 88, 88, 98, 99.

Now, as we can see in the data above that the maximum value is the last value in our data and the minimum value is the first value in our data.

So, the maximum value is 99 and the minimum value is 42.

Now, the mean of the data is given by the following formula;

Mean = $\frac{\sum X}{n}$

          = $\frac{42+ 56+ 62+ 64+ 72+ 75+ 75+ 75+ 85+ 85+ 87+ 88+ 88+ 98+ 99}{15}$

          = $\frac{1151}{15}$ = 76.73

Now, the mode is the value that occurs the maximum number of times in our dataset which is 75 as it is appearing the maximum (3) number of times in our data.

So, the mode of the data is 75.

Now, for finding the median, the number of observations is odd (i.e. 15);

So, Median = $(\frac{n+1}{2})^{th} \text{ obs.}$

                   = $(\frac{15+1}{2})^{th} \text{ obs.}$

                   = $8^{th} \text{ obs.}$ = 75

Hence, the median of the data is 75.