1.) which of the following is the value of the range?
a. 31
b. 35
c. 34
d. 27
2.) what is the average deviation?
a. 6.30
b. 8.38
c. 2.86
d. 3.60
3.) which of the following shows the correct way of calculating variance?
a. s 2 = σfd 2 n−1 = 2 880 49 = 2 880 50−1 ≈ 58.78
c. s 2 = σfd 2 n−1 = 2 882 49 = 2 882 50−1 ≈ 58.82
b. s 2 = σfd 2 n−1 = 2 880 50−1 = 2 880 49 ≈ 58.78
d. s 2 = σfd 2 n−1 = 2 882 50−1 = 2 882 49 ≈ 58.82
4.) using the table above, which of the following is the standard deviation of the given data?
a. 6.77
b. 7.76
c. 7.67
d. 0.767
Answers
Solution:
1) Range= Highest value-lowest value
= 49-15
= 34
Range=34 (c)
2) Average deviation= 1/N ∑i=1n∣xi−m∣
=1/7 ×60.6
=
= 8.65
Average deviation=8.65 (b)
3) Variance=
= 58.82
s 2 = σfd 2 n−1 = 2 882 50−1 = 2 882 49 ≈ 58.82 (d)
4) Standard deviation=
=
= 7.67
Standard deviation=7.67 (b)
Final answer:
1) c
2) b
3) d
4) b
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Answer:
Using the formulae of statistics, we can find that the range of the given interval is 34, while the average deviation of the interval is 8.65, with its variance being 58.82 and the standard deviation being 7.67.
Step-by-step explanation:
1. The range of any interval is the difference between its highest and lowest values.
Thus, the range of the given interval is 34.
Because, range = highest value - lowest value
range = 49-15
range = 34
2. The average deviation is calculated with its respective formula, which is - 1/N ∑∣xi−m∣
A = 1/7 x 60.6
A = 8.65
3. Variance is defined as the sum of all the frequencies divided by the total number of frequencies minus 1.
Variance = sum/(n-1)
= 2882/(50-1)
Variance = 58.82
4. The standard deviation can be found from the following formula -
Standard deviation = √(variance)
= √58.82
Standard deviation = √7.67
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