Question

2. Determine the following characteristics of the sample data 3 5 6 15 27 43 515 3 a. Mean: X - b. Standard deviation: S l.10 c. Number of data values, n: IS+ 2 d. Mode : Y3 S5 3. Characteristics from a sample are called 11 Sct 4. Characteristics from a population are calledSmds deuat 5. Three types of frequency distributions are: 6. What type of frequency distribution is the data from problem #2. oune

Answer 1

xi	fi	fi * xi	fi * xi2
3	15	45	135
5	27	135	675
6	43	258	1548
Total	85	438	2358

2 (a)

Mean = $\sum f_i x_i /\sum f_i$ = 438 / 85 = 5.152941

(b)

Standard deviation is given as,

$\sqrt{\frac{\sum f_ix_i^2}{ \sum f_i} - \left ( \frac{ \sum f_ix_i}{ \sum f_i} \right )^2} = \sqrt{\frac{2358}{85}-\left ( \frac{438}{85} \right )^2}$

= 1.090126

(c)

Number of data values = $\sum f_i$ = 85

(d)

Mode is the value of xi for the maximum value of fi. The maximum value of fi is 43.

So, the mode is 6.

3.

Characteristics from the sample are called Statistics.

4.

Characteristics from the population are called parameter.

5.

Three types of frequency distributions are - Grouped, Ungrouped, Categorical

6.

Xi is a quantitative variable and there is no range of xi for each frequency. So, the type of frequency distribution is Ungrouped