İSTATİSTİK I

In order to find the mode of this raw data, first, let’s order the data from smallest to largest as follows 3,3,4,5,6,6,6,7

The number 3 is repeated 2 times, 4 is repeated 1 time, 5 is repeated 1 time, 6 is repeated 3 time, 7 is repeated 1 time. Therefore, for this data set, it can be said that the mode is 6. The answer is B.

In order to find the mode of this raw data, first, let’s order the data from smallest to largest as follows 2,3,3,3,4,4,5,6,6,6,7

The number 2 is repeated 1 time, 3 is repeated 3 times, 4 is repeated 2 time, 5 is repeated 1 time, 6 is repeated 3 time, 7 is repeated 1 time. Therefore, for this data set, it can be said that there are two modes and these modes are 3 and 6. The answer is E.

In order to find the median of this raw data, first, let’s order the data from smallest to largest as follows 3,3,4,5,6,6,6,7

The location of the median in this ordered data is (8+1)/2 = 4,5th observation. Therefore, we
need to identify the 4th and 5th observations’ values in the ordered data, these are 5 and 6 respectively.

The Median is equal to (5+6)/2 = 5,5

The answer is B.

There are 8 observation in this data set. The sum of all the observation result's values is 6+7+3+4+3+5+6+6 = 40

If we divide this value by the number of observation, which is 8, we will find 40/8 = 5 which is the arithmetic mean of this data set. The answer is C.

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.