Chapter 10.1, Problem 1CYU

To determine

To calculate mean median and mode of the student concession.

Answer to Problem 1CYU

Mean is 2.73, median is 3 and mode is 2.

Explanation of Solution

Given information: Student working at the concession stand each hour data,

Hours	Number of student
1	3
2	8
3	6
4	4
5	2

Formula used:

Mean formula is,

  $\overline{X}=\frac{{\displaystyle \sum f{x}_i}}{N}$

Where, f is frequency

N is total number of observation

X is observation.

Median formula is,

  $M=SizeOf{(\frac{N+1}{2})}^{th}item$

Where, N cumulative frequency

Mode is,

  $Mode=ObservationWithHighestFrequency$

Calculation:

Hours	Number of students	fX	CF
1	3	3	3
2	8	16	19
3	6	18	37
4	4	16	53
5	2	10	63
Total	23	63

For mean,

Substituting the values in the mean formula,

  $\overline{X}=\frac{63}{23}$

0n solving,

  $\overline{X}=2.73$

Hence, mean is 2.73

For median,

Substituting the value of cumulative frequency,

  $M=\frac{63+1}{2}$

So,

  $M=\frac{64}{2}$

On solving,

  $M={32}^{nd}term$

Comparing with the table to find 32^nd term,

M= 3

For mode,

Substituting the value of the observation with highest frequency,

  $Mode=2$

Median is best for this type of data, as median is best to represent grouped data. Since, the data is highly skewed, mean can give a deceiving value and mode can be really unruly, unless one knows in advance that mode is unique.