İSTATİSTİK I - Deneme Sınavı - 2

Most frequent value(s) is the mode. Middle number in ordered data by magnitude is the median. Average number of values is the arithmetic mean. The answer is B

I. It is defined as the tendency of data to cluster around some random variable value. (True)

II. Some central tendency measures are arithmetic mean, median and mode. (True)

III. Central tendency measures can tell us details about every piece of data. (False, Central tendency measures do not tell us details about every piece of data.)

The answer is C.

The geometric mean is found by taking the square root of all the observation's multiplication. For 4, 10, 25 their multiplication is 4*25*10=1000 and the cubic root of 1000 is 10. The answer is A.

Midrange is an arithmetic mean of the extremes in both end of the data set. It only needs the smallest
value and the largest value to be given. The arithmetic mean of the maximum and minimum value of the set gives the midrange. For the set 6,7,3,4,3,5,6 the minimum value is 3 and the maximum value is 7 therefore the midrange would be equal to (7+3)/2 = 5. The answer is A.

The Winsorized mean can be calculated with the remaining values after replacing a certain number or the proportion of the values at the low and high end of the sorted data. First the data set is ordered from smallest to largest 3,3,4,5,6,6,7 then we will find how many data points will be replaced, k, since the winsorizing is 30% and there are 7 observations, the value of k is k = np = 7×0.30 = 2,1 which is nearly 2. Therefore, 2 observation from each end of the sorted data will be replaced with those next in magnitude, these observations are as follows, 3 is replaced with 4 and 7 and 6 is replaced with 6. The set yields to 4,4,4,5,6,6,6. The 30% Winsorized mean of the data set is (4+4+4+5+6+6+6)/7= 5. The answer is D.

The trimmed or as it may sometimes be called as the truncated mean is a slightly modified version of the
arithmetic mean. Trimmed or truncated mean is calculated after a certain number or proportion of the lowest and highest observations from the sorted data are removed (trimmed) from the calculations. First, the data is ordered from smallest to largest, as follows, 2,3,4,5,6,6,7. Then we will find how many data points will be discarded, k, since the trimming is 30% and there are 7 observations, the value of k is k = np = 7×0.30 = 2,1 which is nearly 2. Therefore two 2,3,6 and 7 is removed from the set, which yields to 4,5,6. The sum, 15 is divided to n − 2k which is equal to 7 - 2*2=3 this results in the value 5.The answer is D.

The most repeated value is 4, therefore the mode is 4.

The highest frequency (18) is observed for 45, therefore mode is 45.

If a data set has more than one mode, it refers to a multimodal distribution, indicating the frequencies of several observations with the similar highest frequencies. Specifically, when two values have the highest frequency in the data as in 1, 2, 2, 3, 4, 4, 5, 6, it is called as bimodal (2 and 4) distribution.

The data is already ordered. There are 10 observations:

(10+1)/2 = 5.5

so the median is the arithmetic mean of 5th and 6th observations:

median =(5 +6)/2=5.5

mean = total / n

mean = 73 / 10

mean = 7.3

'Mean' refers to the average of a set of numbers in the data. The correct answer is C.

The median is the middle value of an ordered dataset. The correct answer is A.

The mode is the main centrality measure for nominal scales. The correct answer is A.

Mode is the most frequent value in the entire data. The correct answer is D.