What is the type of distribution, center, and spread of the data?
5 6 5 6 4 4 3 3 5 6 8 12
a. Skewed right; median: 5; interquartile
range: 2
c. Skewed left; median: 5; interquartile
range: 2
b. Normal; mean: 5.6; standard deviation:
2.7
d. Normal; median: 6; interquartile range: 2
To determine the type of distribution, center, and spread of the data, we can analyze the given data set: 5, 6, 5, 6, 4, 4, 3, 3, 5, 6, 8, 12.
To start, we can calculate some basic statistics.
1. Distribution: By observing the data, we see that it is not perfectly symmetrical around a central value. It has some values that are more frequent than others. In this case, the data is centered around 5 and contains some lower values but no higher values. This indicates that the data is skewed right, meaning it has a longer tail on the right side.
2. Center: The median of a data set, also known as the central value, is the number that separates the top 50% of the data from the bottom 50%. To determine the median, we can arrange the data in numerical order: 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 8, 12. As there are 12 values, the median will be the average of the 6th and 7th values, which are both 5. Therefore, the median (central value) of the data is 5.
3. Spread: The spread of the data can be measured by calculating the interquartile range (IQR). The IQR is the range between the 25th and 75th percentiles of the data. To calculate the IQR, we first need to find these percentiles. As the data set has 12 values, the 25th percentile will be the value at the 3rd position (counting from the lowest), which is 4. The 75th percentile will be the value at the 9th position, which is 6. Therefore, the IQR is 6 - 4 = 2.
Based on these calculations, the correct answer is:
a. Skewed right; median: 5; interquartile range: 2.