Question

(1) These are the sales prices of recent home sales at a real estate office:

$475,000 $310,000   $350,000    $400,000   $475,000   $1,000,000   $390,000

Find the x̄, median and the mode for the prices. In your opinion, which is the best

measure of central tendency for this data set? Why?

(2) Identify the population, parameter, sample, and statistic in the statistical study quoted below. What type of data was gathered in the study?

The United Hospital Fund recently examined the cases of 1,254 randomly chosen patients of New York city hospitals. The researchers determined that in 25.8% of the cases, hospitalization could have been avoided with timely outpatient care. The percentage varied from a high of an estimated 59.5% of cases in East Harlem to a low of 12.4% of cases in an Upper East Side hospital.

(3) Find the mean, median, and mode for the data on the number of sick days used for a group of employees below:

Number of sick days taken in the last year	Frequency
0	11
1	25
2	20
3	14
4	6
5	3
9	1

Answer 1

Question 1) Solution:

We have given data in increasing order,

310000,350000,390000,400000,475000,475000,1000000

Sample size:7

Mean (x?): 485714.287
Median: 400000
Mode: 475000

First quartile: 350000
Third quartile: 475000

Q3-Q2 = 475000 - 400000 = 75000

Q2-Q1 =400000 - 350000 = 50000

Q3-Q2 > Q2-Q1

Therefore, given data is positively skewed.

Median is the best measure of central tendency for this data set.

Therefore, for skewed data median can be better measure than mean.

Question 2) Solution:

Population = patients of New York city hospitals.

Parameter = proportion of patients in New York city hospitals for whom hospitalization could be avoided with timely outpatient care.

Sample = examined the cases of 1,254 randomly chosen patients of New York city hospitals.

Statistic = Statistic is the estimates the parameter) = 25.8% ................Statistic is the sample proportion

Question 3) Solution: