Chapter 10.1, Problem 7PPS

i.

To determine

To calculate mean, median and mode of the given data set

Answer to Problem 7PPS

Mean is 342.37, Median is329.97 and Mode is259.95.

Explanation of Solution

Given information:Prices of comparable computer tablets at 10 different locations is,

Tablet prices($)

289.95,259.95,310,349.95,459.95,399.95,259.95,300,389,405

Formula used:Mean formula is,

Mean= $\frac{{\displaystyle \sum _{i=1}^n{X}_i}}{n}$

Where, n=total number of terms,

  ${\displaystyle \sum _{i=1}^n{X}_i}$ = sum of all terms

Median formula is,

Median= $\frac{(\frac{N^{th}}{2})term+(\frac{N}{2}+1)term}{2}$

Mode formula is,

  $Mode=ObservationWithHighestFrequency$

Calculation:

Re-arrange the terms in ascending order,

259.95, 259.95, 289.95, 300, 310, 349.95, 389, 399.95, 405, 459.95

For mean,

Substituting values in mean formula,

  $mean=\frac{289.95+259.95+310+349.95+459.95+399.95+259.95+300+389+405}{10}$

So,

  $mean=\frac{3423.7}{10}$

On solving,

  $mean=342.37$

Hence, mean is 342.37

For Median,

Number of observation,

n = 10

Substituting the values in median formula,

  $median=\frac{(\frac{{10}^{th}}{2})term+(\frac{10}{2}+1)term}{2}$

On solving,

  $median=\frac{5^{th}term+6^{th}term}{2}$

Substituting the values of 5^th and 6^th term,

  $median=\frac{310+349.95}{2}$

On solving,

  $median=329.97$

For Mode,

Substituting the value in mode formula,

  $Mode=459.95$

ii.

To determine

To evaluate the better measure of centre.

Answer to Problem 7PPS

Median is the better measure of center.

Explanation of Solution

Given information:

Mean, median and mode.

Median is a better measure of center in case someone wants to buy one tablet. As unlike mean it won’t be affected by the highly skewed data and unlike mode will not result in the highest price. Median will provide with a price, which will not be affected by the too high or too low values in the data set