PART - A 1. (11pts) A data set contains the observations 2, 3, 5,

PSY 103
Statistics in Social Sciences
Midterm Exam
PART - A
1. (11pts) A data set contains the observations 2, 3, 5, -7, -2, 4, 8. Find ∑
Answer:
3 pts
3pts
5 pts
171
169
146,857
;
2. (11pts) A data set contains the observations
Answer:
(∑ ) ; ∑(
;
. Find ∑
(∑ ) ; ∑(
3 pts
3pts
5 pts
1,298
0,68
1,18
3. (6pts) A data set contains the observations 1, 3, 7, 9, 11, 13. Find ∑
̅)
̅)
(∑ )
6 pts
Answer:
107,33
4. (18pts) A data set contains the observations -2, -3, -4, 0, 0, 1, 2, 4, 4, 5, 6, 10, 11, 12.
Find mean, median, mode, range, sample variance, standart deviation. What about skewness?
Answer:
Mean (3pts)
Median
(3 pts)
3,28
3
Mode (2pts)
Range
(2pts)
Sample
Variance
(5 pts)
Standart
Deviation (2pts)
Skewness
(1 pts)
0 ve 4
16
24,34
4,93
Right
5. (5pts) For a quantitative data set that contains at least five observations, show that ∑(
Observations
_1_, _2_, _3_, _4_,
_5_
̅)
Calculations
Average: (1+2+3+4+5)/5=3
(1-3)+(2-3)+(3-3)+(4-3)+(5-3)=-2-1+0+1+2=0
6. (6pts) Assume that you are being asked to calculate the variance of a given sample. And you have
the formula for this task (On page 4, second formula). But why is that formulated the way it is written.
Explain the function of numerator, and denominator.
Answer: According to question #5, if we take the summation without squares we get zero, and there
is nothing to do more, if you have started with nothing but zero. So we basically sum of the squared
deviations from the mean for every measurements, and it makes sense. For the denominator, we do
the trick called correction term making the result bigger for the sample standart deviation dividing by
(n-1) rather than n. Because it tends to be bigger when we measure standart deviation for sample
measurements rather than population. In population n goes bigger and bigger like n >> 1 etc.
1
PSY 103
Statistics in Social Sciences
Midterm Exam
7. (4pts) The mean ̅ of a data set is 35,4 and the sample standart deviation s is 3,7. Find the interval
representing measurements within three standart deviations of the mean.
4 pts
Answer:
(24,3 ile 46,5)
8. (12 pts) The following is a list of 20 measurements. How many of the measurements fall within one
standart deviation of the mean?
12
11
18
13
14
14
17
16
19
18
16
15
14
13
18
17
15
15
17
19
12 pts
Answer:
11 out of 20 measurements
PART - B
(13 pts) Fill in the blanks in the following table with the word given below. (Each questions is 2 points)
9. A class frequency is the number of observations in the data set that fall into a particular class.
10. A class is one the categories into which qualitative data can be classified.
11. A data set is said to be skewed if one tail of the distribution has more extreme observations than the
other tail.
12. A population is a set of units (usually people, objects, transactions, or events) that we are interested in
studying.
13. A sample is a subset of the units of a population.
14. A variable is a characteristic or property of an individual experimental (or observatinal) unit in the
population.
15. Qualitative data are measurements that cannot be measured on a natural numerical scale; they can only
be classified into one of a group of categories.
16. Quantitative data are measurements that are recorded on a naturally occurring numerical scale.
17. The class relative frequency is the class frequency divided by the total number of observations in the data
set.
18. The mean of a set of quantitative data is the sum of the measurements, divided by the number of
measurements contained in the data set.
19. The median of a quantitative data set is the middle number when the measurements are arranged in
ascending (or descending) order.
20. The mode is the measurement that occurs most frequently in the data set.
21. The range of a quantitative data set is equal to the largest measurement minus the smallest
measurement.
variable, skewed, sample, range, quantitative data, qualitative data, population,
mode, median, mean, class relative frequency, class, class frequency
2
PART - C
22
Bar graph for type of aphasia Pareto Diagram for type of aphasia
Stem-and-Leaf display for 100
mileage ratings
Histogram for 100 EPA gas mileage
ratings
Numerical descriptive measures
Center
(6 pts) “Spread // Stem and Leaf // Histogram // Pareto Diagram // Bar Graph // Center”
Spread
PART - D
(8 pts)True/False Questions.
23) (T) The bars in a bar graph can be arranged by height in ascending order from left to right.
24) (T) Either vertical or horizontal bars can be used when constructing a bar graph.
25) (F) If 25% off statistics class is sophomores, then in a pie chart representing classifications of the students in your statistics
class the slice assigned to sophomores is 190 degrees.
26) (F) The slices of a pie chart must be arranged from smallest to largest in a clockwise direction.
27) (F) Class relative frequencies must be used, rather than class frequencies or class percentages, when constructing a Pareto
diagram.
28) (F) A Pareto diagram is a pie chart where the slices are arranged from largest to smallest in a counterclockwise direction.
29) (F) All class intervals in a histogram have different widths.
30) (T) A histogram can be constructed using either class frequencies or class relative frequencies as the heights of the bars
3
PSY 103
Statistics in Social Sciences
Midterm Exam
Sorular için gerekli açıklamalar ve formüller:
A-Bölümü (73 Puan)
1. Verilen veri seti için toplam işaretleri ile gösterilen üç işlemin sonucunu yazınız.
2. Verilen veri seti için yine toplam işaretleri ile gösterilen üç işlemin sonucunu yazınız.
3. Verilen veri seti için toplam işareti ile gösterilen işlemin sonucunu yazınız.
4. Verilen veri seti için ortalamayı, ortancayı, modu, aralığı, örneklem varyansını, standart
sapmayı bulunuz. Ve eğrinin çarpıklığı (skewness) hakkında bilgi veriniz.
5. Toplam sembolü ile gösterilen eşitliğin doğru olduğunu, oluşturacağınız en az beş elemanlı herhangi
bir nicel veri seti ile kanıtlayınız. İşlemleri sorunun altında açık bir şekilde gösteriniz.
6. Örneklem için varyans değerini hesaplamaya yarayan formülü dikkate alınız. (Sayfa-4’te 2 nolu
formülden bahsediyor). Formül neden bu şekilde bir yapıya sahiptir? Pay (karesi alınan ifade) ve
paydadaki (n-1’li ifade) hesaplamaları dikkate alarak iki cümle ile açıklayınız. Türkçe yanıt
verebilirsiniz.
7. Ortalaması ve standart sapması verilen bir veri setinde, ortalamadan üç standart sapma
aralığındaki değerlerini bulunuz.
8. Soruda verilen 20 tane ölçümü göz önüne alınız. Bu ölçümlerden kaç tanesi ortalamadan bir standart
sapma aralığındadır, yazınız. Bu aralıkta bulunan sayıların kaç tane olduğunu yazmanız yeterli.
B-Bölümü (13 Puan)
9. 9-21 arasındaki 13 soruda, tablonun altında verilen kelimeleri, tablodaki tanımlara karşılık gelecek
şekilde eşleştiriniz. Kelimeleri tabloda uygun yerlere yazınız.
C-Bölümü (6 Puan)
22. Soruda verilen grafiklerin türlerini üzerindeki açıklamalarda boş bırakılan yerlere yazınız. En
sağdaki grafikte a ve b ile gösterilen aralıklar nedir, boşluğa yazınız. Kelimeler grafiklerin altında.
D-Bölümü (8 Puan)
23. 23-30 arasındaki sorulara doğru ise T, yanlış ise F harfi koymanız yeterli.
Not: Bazı sorularda (1,2,3,4,5 ve 8) çözüm adımlarını göstermeniz gerekmektedir.
Bunun için size verilen karalama kağıdını kullanın. BAŞARILAR.
Formula for sample mean:
1
Formula for the sample variance:
3
2
4
∑
(
̅)
4