Chapter 10.1, Problem 11PPS

a.

To determine

To calculate mean practice time of D.

Answer to Problem 11PPS

D’s mean practice time is 21 mins 54 secs.

Explanation of Solution

Given information: D’s practice times (m: s),

20:45, 21:30, 21:15, 22:32, 21:40

Formula used: Mean formula is,

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

Where, n=total number of terms,

Calculation:

Convert time in seconds,

Now, Practice time is 1245, 1290, 1275, 1352, 1300

Substituting the values in mean formula,

  $mean=\frac{1245+1290+1275+1352+1300}{5}$

So,

  $mean=\frac{6462}{5}$

On solving,

  $mean=1292.4$

Hence, the timing of D’s practice is 1292.4 seconds.

Converting seconds into minutes,

  $60\sec =1\min$

Cross multiplying,

  $1\sec =\frac{1}{60}\min$

For 1292.4 seconds,

  $1292.4\sec =\frac{1292.4}{60}\min$

On solving,

  $1292.4\sec =21.54\min$

That is, 21 mins 54 secs.

Hence, D’s mean practice time is 21 mins 54 secs.

b.

To determine

To calculate D’s race time.

Answer to Problem 11PPS

D’s race time is 1260 seconds

Explanation of Solution

Given:

Completion time of race was 30secs less than her median time.

Formula used: Median’s formula is,

Median= $\frac{{(n+1)}^{th}}{2}observation$

Calculation:

Re-arranging her practice time in ascending order,

1245, 1275, 1290, 1300, 1352

Number of terms (n) =5

Substituting the values in median formula,

  $median=\frac{{(5+1)}^{th}}{2}observation$

So,

  $median=\frac{6^{th}}{2}observation$

On solving,

  $median=3^{rd}observation$

Substituting the value of 3^rd term,

  $median=1290$

Hence, her race timings are,

  $RaceTime=Median-30$

Substituting the value,

  $RaceTime=1290-30$

On solving,

  $RaceTime=1260$

Hence, D’s race timings are 1260 seconds