1. For the month of January, a checking account had a balance of $658 for 21 day
ID: 2653105 • Letter: 1
Question
1. For the month of January, a checking account had a balance of $658 for 21 days, $1,832 for 6 days, and $517 for 4 days. Calculate this account’s mean daily balance for January.
2. By cluster sampling, a researcher randomly found annual salaries of a block of residents in Sun City, USA. Below are the salaries rounded to the nearest $1000.
$47, $51, $48, $50, $250, $49, $46, $51.
(a) What is the mean yearly salary for this group of residents?
(c) If the researcher is paid by a newspaper to report the annual salary for residents in Sun City, USA, should the researcher report the mean or the median? Explain your reasoning.
(b) What is the median yearly salary for this group of residents?
3. For the problem in #2, answer the following questions.
(a) What is the standard deviation?
(b) Do you think the standard deviation accurately conveys the average spread of the data about the mean annual salary? Explain your reasoning.
Explanation / Answer
Answer: 1. Account’s mean daily balance for January:
Mean = [(658*21)+ (1832*6)+ (517*4)]/(21+6+4) =$ 867.03
Answer:2 (a) The mean yearly salary for this group of residents is
Mean = ($47+ $51+ $48+ $50+ $250+ $49+ $46+ $51)/8
=74
Answer:2 (b) Median = (N+1)/2
=(8+1)/2
=4.5 items
Arrange in ascending series = 46,47,48,49,50,51,51,250.
Median is = 4 item +(5 item - 4 item)
=49+(50-49)
=50
Answer:2(c) The researcher should report the mean becasuse this mean value might not be the best way to accurately reflect the typical salary. The mean is being skewed by the two large salaries. Therefore, in this situation, we would like to have a better measure of central tendency. As we will find out later, taking the median would be a better measure of central tendency in this situation.
Answer:3 (a) standard deviation = square root of [(46-74)2+(47-74)2+(48-74)2+(49-74)2+(50-74)2+(51-74)2+(51-74)2+(250-74)2]/8
=square root of [784+729+676+625+576+529+529+30976/8]
=66.54
Answer:3 (b) Yes, the standard deviation accurately conveys the average spread of the data about the mean annual salary because
The most commonly reported measure of variability or spread is the standard deviation (SD). The SD is also called the "root-mean-square deviation", which describes the way it is calculated. The operations root, mean, and square are applied in reverse order to the deviations--the individual differences between the observations and the mean.
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