Problem 15BSC

In Exercise, find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. Express answers with the appropriate units of measurement. Then answer the given questions.

Years to Earn Bachelor’s Degree Listed below are the lengths of time (in years) it took for a random sample of college students to earn bachelor’s degrees (based on data from the National Center for Education Statistics). Based on these results, does it appear that it is common to earn a bachelor’s degree in 4 years?

4 4 4 4 4 4 4.5 4.5 4.5 4.5 4.5 4.5 6 6 8 9 9 13 13 15

Problem 15BSC

Answer:

Step1 of 3:

We have Listed below are the lengths of time (in years) it took for a random sample of college students to earn bachelor’s degrees (based on data from the National Center for Education Statistics).

4 |
4 |
4 |
4 |
4 |
4 |
4.5 |
4.5 |
4.5 |
4.5 |
4.5 |

4.5 |
6 |
6 |
6 |
8 |
9 |
9 |
13 |
13 |
15 |

Step2 of 3:

We need to find the (a)mean, (b) median, (c) mode, and (d) midrange for the given sample data. Express answers with the appropriate units of measurement. Then answer the given questions.

Step3 of 3:

a)Mean:mean is the average of the numbers and it is given by

Mean() =

=

=

= 2.175

Therefore,the mean of the given data is 2.175 years.

b).Median:The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

Write the given data in Ascending order

4 |
4 |
4 |
4 |
4 |
4 |
4.5 |
4.5 |
4.5 |
4.5 |
4.5 |

4.5 |
6 |
6 |
6 |
8 |
9 |
9 |
13 |
13 |
15 |

Median = mid value in a given data, if the given data is odd

= 4.5

Therefore,the median of the given data is 4.5 years.

c)Mode:The mode is the value that appears most often in a set of data. The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.

Here, 4 and 4.5 are repeated six times hence the mode is 4 years and 4.5 years

Therefore, Mode = 4 years and 4.5 years.

d).Midrange:the midrange or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set, defined as: The mid-range is the midpoint of the range

Mid-range =

=

=

= 9.5

Therefore,midrange of the given data is 9.5 years.

It is common to earn a bachelor’s degree in four years, but the typical college student requires more than four years.