Quiz answers on the shape and properties of a normal distribution! #22
Quick revision of the basics!
Hello Everyone,
If you remember, I sent two Quizzes on Normal distribution in the previous weeks. The answers of one of the quizzes have already been shared in my last week’s newsletter. Today, I’ll discuss about the answers of the second quiz. Just in case, you missed any of these, here are the links:
Answers to Quiz 2: Today’s newsletter
You can add your insights by using the “Leave a comment” button after each question.
1. Does changing the mean value while keeping standard deviation constant, change the shape of the distribution?
Yes
No
Answer: No
Explanation: Mean determines the centre and standard deviation determines the spread of a normal distribution. So, changing the mean value doesn’t change the shape of the distribution if standard deviation is constant. If you increase the mean value, the distribution curve will move to the right and if you decrease the mean value, the distribution curve will move to the left, on the x-axis.
2. Does changing standard deviation while keeping mean value constant, change the shape of the distribution?
Yes
No
Answer: Yes
Explanation: Since standard deviation determines the spread of the distribution around the mean, changing it will change the shape of the distribution. A large standard deviation means the data is more spread out around the mean. A smaller standard deviation means the data is clustered closely the mean.
So, If you increase the standard deviation, the distribution curve will look flatter and wider. If you decrease the standard deviation, the distribution curve will look narrower and taller.
3. Decreasing mean value shifts the curve to the __________ on the x-axis.
Left side
Right side
Can’t predict
Doesn’t change anything
Answer: Left side
Explanation: Since mean determines the centre of a normal distribution, decreasing mean value shifts the distribution curve to the left side on the x-axis.
4. Increasing mean value shifts the curve to the __________ on the x-axis.
Left side
Right side
Can’t predict
Doesn’t change anything
Answer: Right side
Explanation: Since mean determines the centre of a normal distribution, increasing mean value shifts the distribution curve to the right side on the x-axis.
5. In a positively skewed distribution, the mean lies to the ______ of the median.
Left
Right
Same position
Can’t predict
Answer: Right
Explanation: Mean and median both comes under the measures of central tendency of a dataset, but they have different properties.
Mean is the sum of all the values divided by total number of values in the dataset. It is also known as the average value and is sensitive to outliers. Median is the middle of the dataset when the values are arranged in ascending or descending order. It is robust to outliers.
In a positively skewed distribution, most of the values are clustered on the left side which makes median to be closer to the left side (near the peak) and some of the larger values stretches the tail on the right side which pulls mean to the right side, beyond the median.
6. In a negatively skewed distribution, the mean lies to the ______ of the median.
Left
Right
Same position
Can’t predict
Answer: Left
Explanation: Same explanation as mentioned in Question no.5, just replace right with left in the description.
7. In a perfectly symmetrical distribution, the mean lies to the ______ of the median.
Left
Right
Same position
Can’t predict
Answer: Same position
Explanation: In a perfectly symmetric distribution, mean=median=mode. So, mean and median lies at the same position.
8. As you move away from the mean in either direction, the probability ________ .
Stays the same
Increases
Decreases
Becomes negative
Answer: Decreases
Explanation: It can be observed by looking at the bell curve formed by a normal distribution. Mean is at the centre of the distribution and it corresponds to the peak. As you move away from the mean in any direction, the probability starts decreasing.
9. What is meant by a distribution is positively skewed?
Mean = Median
The distribution is symmetric
The left tail is longer
The right tail is longer
Answer: The right tail is longer
Explanation: It happens because there are few values extremely larger than rest of the values in the dataset. These values are known as outliers and they extend the tail on the right side.
10. What is meant by a distribution is negatively skewed?
The probabilities become negative
Mean = Median
The left tail is longer
The right tail is longer
Answer: The left tail is longer
Explanation: It happens because there are few values extremely smaller than rest of the values in the dataset. These values are known as outliers and they extend the tail on the left side.
Do you want more of such QUIZ newsletters in future?
Job openings
I recently shared posts regarding multiple job openings in AI/ML domain. Check them out using following links:
https://www.linkedin.com/feed/update/urn:li:activity:7234849243344068608/
https://www.linkedin.com/feed/update/urn:li:activity:7234842049265475586/
Should I share job opening in upcoming newsletters?
Curious about a specific AI/ML topic? Let me know in comments.
Also, please share your feedbacks and suggestions. That will help me keep going. Even a “like” on my posts will tell me that my posts are helpful to you.
See you soon!
-Kavita
P.S. Let’s grow our tribe. Know someone who is curious to dive into ML and AI? Share this newsletter with them and invite them to be a part of this exciting learning journey.