Consider the following frequency distribution.

Class Frequency
2 up to 4 32
4 up to 6 48
6 up to 8 92
8 up to 10 32
a.
Calculate the population mean. (Round your answer to 2 decimal places.)

Population mean
b.
Calculate the population variance and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Population variance
Population standard deviation

Restating the Frequency distribution clearly

Class                             Frequency

2 up to 4                       32

4 up to 6                       48

6 up to 8                       92

8 up to 10                      32

a. Population mean (μ) = 6.22

b. Population Variance = 3.88

c. Standard deviation = 1.97

Step-by-step explanation:

1. To solve this, we first of all have to form a frequency table, and in order to get the different components of the table, we have to state the formula of the most complex part of the question that is the standard deviation

Standard deviation (S) =√ [∑f(m-μ)² / ∑f - 1].

2. next, we will form the frequency table as shown below making sure to include all the components of the standard deviation formula.

Class      f      m      f×m      μ          (m-μ)      (m-μ)²         f(m-μ)²

2-4        32     3       96      6.22       -3.22    10.3684       331.7888

4-6        48     5       240    6.22        -1.22    1.4884         71.4432

6-8        92     7       644    6.22         1.22     1.4884         136.9328

8-10       32     9       288   6.22         2.78     7.7284        247.3088  

            204           1268                                                     787.4736

where:

f = frequency

m = midpoint

μ = mean

3. After getting f, and m, we can calculate the mean which is also known as the average value, as shown below:

mean (μ) :  ∑(f × m) / ∑f          Note that the symbol "∑" stands for "sum of"

∴ μ =   = 6.2157  

Rounding to 2 decimal places μ = 6.22

4. Next let us define what standard deviation is; the standard deviation is the extent to which a value differ from the mean value. The formula is shown below.

Standard deviation (S) =√ [∑f(m-μ)² / ∑f - 1]

S  

∴ S = 1.97 (to 2 decimal places)

5. finally, the variance is the square of the standard deviation and it is shown thus:

Variance (S²) = = 3.88 (2 decimal places).

step-by-step explanation: