Download 1. For a particular sample of 63 scores on a psychology exam, the

1. For a particular sample of 63 scores on a psychology exam, the following results were
obtained.
First quartile = 47 Third quartile = 81 Standard deviation = 11 Range = 68
Mean = 70 Median = 71 Mode = 77 Midrange = 55
Answer each of the following:
I. What score was earned by more students than any other score? Why? 77
II. What was the highest score earned on the exam? 89
III. What was the lowest score earned on the exam? 21
IV. According to Chebyshev's Theorem, how many students scored between 48 and 92?
48 students
V. Assume that the distribution is normal. Based on the Empirical Rule, how many students
scored between 59 and 81? 41 students
Please show all of your work.
2. Find the range, standard deviation, and variance for the following sample data:
2, 11, 81, 29, 22, 59, 78, 71, 21, 43, 99, 12, 38, 74, 56, 81
Range= 97; variance=915.73; Stdev=30.26
3. In terms of the mean and standard deviation:
- What does it mean to say that a particular value of x has a standard score of +3.1?
x is 3.1 standard deviations above the mean (that is, x=mean+3.1*stdev)
- What does it mean to say that a particular value of x has a z-score of -1.0?
x is 1 standard deviation below the mean (that is, x=mean-1*stdev)
4. A student scored 95 percent on a test, and was in the 90th percentile. Explain these two
numbers.
Suppose the maximum score is 100 and there were 200 students who took the test.
Then there were 20 students who scored 95 or better.
5. An animal trainer obtained the following sample data (Table A) in a study of reaction times of
dogs (in seconds) to a specific stimulus. He then selected another group of dogs that were much
older than the first group and measured their reaction times to the same stimulus. The sample
data is shown in Table B.
Table A
Classes Frequency
2.3-2.9 21
3.0-3.6 02
3.7-4.3 15
4.4-5.0 10
5.1-5.7 04
5.8-6.4 30
Table B
Classes Frequency
2.3-2.9 05
3.0-3.6 03
3.7-4.3 40
4.4-5.0 39
5.1-5.7 05
5.8-6.4 05
Find the variance and standard deviation for the two distributions above. Compare the variation
of the data sets. Decide if one data set is more variable than the other.
Variance A = 2.0087, StdevA =1.4173
Variance B= 0.51136, StDEv B= 0.7151
The first data set is more variable than the second
6. In each of the four examples listed below, one of the given variables is independent (x) and
one of the given variables is dependent (y). Indicate in each case which variable is independent
and which variable is dependent.
I. Cost to ship; Size of package
independent dependent
II. Geographic location; Average annual snowfall
III. Length of ride; Taxi fare
IV. DNA of offspring; DNA of parents
7. A sample of purchases at the local convenience store has resulted in the following sample data,
where x = the number of items purchased per customer and f = the number of customers.
x12345
f 7 17 8 8 7
What does the 17 stand for in the above table? Number of customers who bought exactly 2 items
Find the midrange of items purchased. Midrange = (max+min)/2 =(1+5)/2 =3
How many items were purchased by the customers in this sample? 132
8. Suppose we have a set of blood pressures with a mean of 120 Systolic, and a sample standard
deviation of 20 points. If we assume a normal distribution of Systolic blood pressures, then
between what two values can we be assured 99.7% of all Systolic blood pressures will lie?
Between 60 and 180
9. Household income does not tend to follow a normal distribution in a particular state, yet
average income is approximately $45,000/year in this state, with a standard deviation of about
$9000. Within what income range would approximately 93.75% of the household incomes lie
within this state? Show all work as to how this is obtained.
Between $28,260 and $61,740
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