The height of 44 students (in centimeter) are presented in the frequency distribution below. Complete the table, and then find the median. Height
182 - 188
175 - 181
168 - 174
161 - 167
154 - 160
147 - 153
140 - 146

Frequency
1
3
6
15
12
4
3

L

Given:

The height of 44 students (in centimeter) are presented in the given frequency distribution.

To find:

The median of the given data.

Solution:

The given intervals are inclusive first make the intervals exclusive by adding 0.5 in upper limit and by subtracting 0.5 from the lower limit.

The complete frequency distribution table is shown below:

Height              Frequency           L                            <cf

182 - 188                  1                  181.5 - 188.5            44

175 - 181                   3                 174.5 - 181.5             43

168 - 174                  6                 167.5 - 174.5            40

161 - 167                 15               160.5 - 167.5            34   Median class

154 - 160                 12                153.5 - 160.5           19

147 - 153                   4                146.5 - 153.5             7

140 - 146                   3                139.5 - 146.5             3

We have, .

The 22th term is include in the class 160.5 - 167.5 because is cf is greater than 22 but the cf of o preceding class is less than 22. So, it is the median class is 160.5 - 167.5.

Formula for median:

Where, l is the lower limit of median class, cf is the cumulative frequency of preceding class, f is the frequency of median class and h is the size of the class.

Now, .

Therefore, the median of the given data table is 161.9.

A) During this time period, Africa was being explored and colonized by various European powers. While the Portuguese were the first to arrive, soon other European powers joined them, such as the French and the Dutch. In these early years of colonialism, these powers fought for dominance in Africa, and borders and areas of control changed frequently.

B) In this passage, we see evidence that supports the idea of the continuous development of the Atlantic in the seventeenth century. We learn about elaborate constructions that the European colonists established along the Atlantic Coast of Africa. We also learn about the importance of trade in this region and of the competition between different European powers.

C) According to this passage, Jean Barbot was a French Protestant and agent of the chartered Senegal Company. In the second paragraph, he makes it clear that this admiration and support lies with the French, and not with the Portuguese. This could be attributed to him being a Protestant. Because of his beliefs, he might feel more attracted by a Protestant nation (the Netherlands) than by a Catholic one (Portugal).