Holooly Plus Logo
Holooly Plus Logo

Question 7.P.4: Compute the standard deviation of this data: 3 2 4 1...

Compute the standard deviation of this data: 3 2 4 1

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

Step 1: Find the mean of the data.
Step 2: Subtract the mean from each data point. These differences should sum to 0.
Step 3: Square each difference and sum the squares.
Step 4: Divide the sum of the squared differences by n – 1.
Step 5: Compute the square root.

Data Step 1
Compute
Mean		 Step 2
Compute
Differences		 Step 3
Square
Differences		 Step 4
Divide Sum
by n – 1		 Step 5
Compute
Square root
3 3 3 – 2.5 =   0.5 0.5² = 0.25
2 2 2 – 2.5 =  -0.5 -0.5² = 0.25
4 4 4 – 2.5 =   1.5 1.5² = 2.25
1 \underline{\qquad1\qquad} \underline{1 – 2.5 =  -1.5} \underline{-1.5² = 2.25} \underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~} \underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}
10/4 = 2.5 0.0 5.00 5/(4 – 1)=1.66667 \sqrt{1.66667}=1.291

 

Related Answered Questions

Question: 7.P.2

A time study analyst wants to estimate the number of observations that will be needed to achieve a specified maximum error, with a confidence of 95.5 percent. A preliminary study yielded a mean of 5.2 minutes and a standard deviation of 1.1 minutes. Determine the total number of observations needed ...

Verified Answer:

a. A maximum error of ± 6 percent of the sample me...
Question: 7.1

A time study analyst wants to estimate the time required to perform a certain job. A preliminary study yielded a mean of 6.4 minutes and a standard deviation of 2.1 minutes. The desired confidence is 95 percent. How many observations will he need (including those already taken) if the desired ...

Verified Answer:

a. s = 2.1 minutes              z = 5 1.96 ...
Question: 7.P.3

Work sampling. An analyst has been asked to prepare an estimate of the proportion of time that a turret lathe operator spends adjusting the machine, with a 90 percent confidence level. Based on previous experience, the analyst believes the proportion will be approximately 30 percent. a. If the ...

Verified Answer:

\hat{p} = .30\qquad ...
Question: 7.4

The manager of a small supermarket chain wants to estimate the proportion of time stock clerks spend making price changes on previously marked merchandise. The manager wants a 98 percent confidence that the resulting estimate will be within 5 percent of the true value. What sample size should she ...

Verified Answer:

When no sample estimate of p is available, a preli...
Question: 7.P.1

A time study analyst timed an assembly operation for 30 cycles, and then computed the average time per cycle, which was 18.75 minutes. The analyst assigned a performance rating of .96, and decided that an appropriate allowance was 15 percent. Assume the allowance factor is based on the workday. ...

Verified Answer:

OT = Average time = 18.75 minutes NT = OT × Perfor...
Question: 7.3

A time study of an assembly operation yielded the following observed times for one element of the job, for which the analyst gave a performance rating of 1.13. Using an allowance of 20 percent of job time, determine the appropriate standard time for this operation. n = 9 PR = 1.13 A = .20 ...

Verified Answer:

1. \mathrm{OT}\;=\;{\frac{\Sigma{x}i}{n}}\;...
Question: 7.2

Compute the allowance factor for these two cases: a. The allowance is 20 percent of job time. b. The allowance is 20 percent of work time. ...

Verified Answer:

A = .20 a. AF = 1 + A = 1.20, or 120% b. \m...